What is the equation of the line that passes through the point left bracket, minus, 3, comma, 3, right bracket
(
−
3
,
3
)
(−3,3) and has a slope of minus, start fraction, 2, divided by, 3, end fraction
−
2
3
−
3
2
?
The equation of a line can be expressed in slope-intercept form as y = mx + b, where m is the slope and b is the y-intercept.
Given that the slope, m, is -2/3 and the point (−3,3) is on the line, we can find the equation of the line.
Using the point-slope form of the equation, we have:
y - y1 = m(x - x1)
Substituting the values of the point (-3,3) and the slope -2/3, we have:
y - 3 = (-2/3)(x - (-3))
y - 3 = (-2/3)(x + 3)
Simplifying the equation:
y - 3 = (-2/3)x - 2
y = (-2/3)x + 1
So, the equation of the line is y = (-2/3)x + 1.
To find the equation of the line, we will use the point-slope form of a linear equation. The point-slope form is given by the equation:
y - y₁ = m(x - x₁)
Where (x₁, y₁) is the given point and m is the slope.
Given point: (-3, 3)
Slope: -2/3
Substituting the values in the point-slope form equation, we get:
y - 3 = (-2/3)(x - (-3))
Simplifying, we have:
y - 3 = (-2/3)(x + 3)
Now, let's distribute the (-2/3) to the terms inside the parentheses:
y - 3 = (-2/3)x - 2
To get the equation in the standard form, we'll move the y term to the right side:
y = (-2/3)x - 2 + 3
y = (-2/3)x + 1
Therefore, the equation of the line that passes through the point (-3, 3) and has a slope of -2/3 is y = (-2/3)x + 1.
To find the equation of a line, we can use the point-slope form of a line: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.
In this case, we have the point (-3, 3) and the slope -2/3.
Step 1: Substitute the given values into the point-slope formula:
y - 3 = (-2/3)(x - (-3))
Step 2: Simplify the equation:
y - 3 = (-2/3)(x + 3)
Step 3: Distribute -2/3 to the terms inside the parentheses:
y - 3 = (-2/3)x - 2
Step 4: Move the constant term to the other side by adding 3 to both sides of the equation:
y = (-2/3)x + 1
So, the equation of the line that passes through (-3, 3) with a slope of -2/3 is y = (-2/3)x + 1.